I do not know the exact circumstances for the alleged obstruction (and whether there was a political or diplomatic purpose to prompt the questioning would be off-topic here) so I have just focused on the relevant legislation in answer to:
What is the law here?
It's not a crime to answer a police question with "I would like to speak to my lawyer"?
But it is a(n alleged) crime to obstruct or otherwise fail to comply with an examination under the Terrorism Act 2000.
This Act is one of a very small number of laws that makes it compulsory for someone to answer questions or provide information, but as they are not under arrest there is no statutory requirement for them to have independent legal advice.
What they say or provide cannot be used against them (with some exemptions, below) and failure to comply is an offence.
A police officer is an examining officer, and under paragraph 2
Schedule 7, Terrorism Act 2000:
(1) An examining officer may question a person to whom this paragraph applies for the purpose of determining whether he appears to be a person falling within section 40(1)(b).
(b) is or has been concerned in the commission, preparation or instigation of acts of terrorism.
Under Paragraph 5:
A person who is questioned under paragraph 2 or 3 must—
(a) give the examining officer any information in his possession which the officer requests;
(b) give the examining officer on request either a valid passport which includes a photograph or another document which establishes his identity;
(c) declare whether he has with him documents of a kind specified by the examining officer;
(d) give the examining officer on request any document which he has with him and which is of a kind specified by the officer.
BUT, under paragraph 5A
(1) An answer or information given orally by a person in response to a question asked under paragraph 2 or 3 may not be used in evidence against the person in criminal proceedings.
(2) Sub-paragraph (1) does not apply—
(a) in the case of proceedings for an offence under paragraph 18 of this Schedule,
(b) on a prosecution for perjury, or
(c) on a prosecution for some other offence where, in giving evidence, the person makes a statement inconsistent with the answer or information mentioned in sub-paragraph (1).
Failure to comply with paragraph 5 is an offence under paragraph 18
(1) A person commits an offence if he—
(a) wilfully fails to comply with a duty imposed under or by virtue of this Schedule,
(b) wilfully contravenes a prohibition imposed under or by virtue of this Schedule, or
(c) wilfully obstructs, or seeks to frustrate, a search or examination under or by virtue of this Schedule.
Once they're arrested on suspicion of this offence then they are entitled to free and independent legal advice under section 58 Police and Criminal Evidence Act 1984.